Angles Math Example 2

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Example 2

medium
Two parallel lines are cut by a transversal. One of the alternate interior angles measures 72°72°. Find all eight angles formed.

Solution

  1. 1
    Alternate interior angles are equal, so both alternate interior angles are 72°72°.
  2. 2
    Each 72°72° angle has a supplementary angle: 180°−72°=108°180° - 72° = 108°.
  3. 3
    By the corresponding angles postulate, the same pattern repeats at both intersections: four angles of 72°72° and four angles of 108°108°.

Answer

Four angles of 72° and four angles of 108°\text{Four angles of } 72° \text{ and four angles of } 108°
When a transversal crosses parallel lines, it creates predictable angle relationships: corresponding angles are equal, alternate interior angles are equal, and co-interior angles are supplementary.

About Angles

The amount of rotation between two rays that share a common endpoint, measured in degrees or radians.

Learn more about Angles →

More Angles Examples

Example 1 easy

Two angles are supplementary. One measures [formula]. Find the other.

Example 3 easy

Two angles are complementary. One measures [formula]. Find the other.

Example 4 medium

An exterior angle of a triangle measures [formula]. One remote interior angle measures [formula]. Fi

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